The third part of this work explores the possibility of employing single dimensional measurements in estimating parameters of an error model that has been developed for multi-dimensional measurements. A mechanism of decomposing single dimensional measurement into multi-dimensional components is developed and augmented to the original model to allow the use of the augmented model in a larger calibration region without an added accuracy requirement to the measurement system. This work also investigates the possibility of using L infinity norm in addition to L2 norm in estimating errors and model parameters.